ThisresearchmonographdevelopstheHamilton-Jacobi-Bellman(HJB)theory viathedynamicprogrammingprincipleforaclassofoptimalcontrolproblems for stochastic hereditary di?erential equations (SHDEs) driven by a standard Brownian motion and with a bounded or an unbounded but fading m- ory. These equations represent a class of in?nite-dimensional stochastic s- tems that become increasingly important and have wide range of applications in physics, chemistry, biology, engineering, and economics/?nance. The wide applicability of these systems is due to the fact that the reaction of re- world systems to...

The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of...